They are equal.
Explanation:
For the law of conservation of energy, the work done when lifting an object by a heigh [tex]\Delta h[/tex] is equal to the gravitational potential energy gained by the object.
In fact:
- the work done when lifting the object is equal to the force applied times the displacement:
[tex]W=Fs[/tex] (1)
however, when the object is lifted at constant speed, the force applied is equal to the weight of the object, mg, while the displacement is equal to the change in height, [tex]\Delta h[/tex]. So, (1) becomes
[tex]W=mg\Delta h[/tex]
But the gain in gravitational potential energy of the object is
[tex]\Delta U=mg \Delta h[/tex]
So, we see that this is equal to the work done.
